Frame the question around bone development.
Two kinds of bone growth: Length comes from endochondral ossification at the growth plate, while width comes from appositional (intramembranous) growth at the periosteum of the shaft. A question about longitudinal growth therefore must point to the growth plate.
What the growth plate is: The epiphyseal plate is a disc of hyaline cartilage sandwiched between the epiphysis and metaphysis. Its zones - resting, proliferating, hypertrophic and calcifying - continuously add cartilage that is replaced by bone, pushing the bone end away and lengthening the bone.
Effect of a fracture there: If a fracture (Salter-Harris type) damages these cartilage zones, the plate may fuse early or unevenly, giving growth arrest, shortening or angulation. This is why physeal injuries in children need careful follow-up.
Why not the others: Epiphysis $\rightarrow$ joint/articular cartilage. Metaphysis $\rightarrow$ remodelling zone of new bone. Diaphysis $\rightarrow$ shaft, widens not lengthens.
Hence the site whose fracture impairs longitudinal growth is the epiphyseal plate (option A).